{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QI2NTXLGH2URNKIPN6UC4QRG6X","short_pith_number":"pith:QI2NTXLG","canonical_record":{"source":{"id":"2404.19719","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-30T17:11:12Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0a518d8d410c9a4554288a814d1b2708d661caa016cb18a6485e12f4620e67f1","abstract_canon_sha256":"ec359d4dee08c966bb9cd909e2e8bb4815354111fdc4bdd59f227de94459e4cf"},"schema_version":"1.0"},"canonical_sha256":"8234d9dd663ea916a90f6fa82e4226f5d32b66ef39fbb7c55765167dab60d2bc","source":{"kind":"arxiv","id":"2404.19719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19719","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19719v2","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19719","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"QI2NTXLGH2UR","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"QI2NTXLGH2URNKIP","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"QI2NTXLG","created_at":"2026-07-05T09:17:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QI2NTXLGH2URNKIPN6UC4QRG6X","target":"record","payload":{"canonical_record":{"source":{"id":"2404.19719","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-30T17:11:12Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"0a518d8d410c9a4554288a814d1b2708d661caa016cb18a6485e12f4620e67f1","abstract_canon_sha256":"ec359d4dee08c966bb9cd909e2e8bb4815354111fdc4bdd59f227de94459e4cf"},"schema_version":"1.0"},"canonical_sha256":"8234d9dd663ea916a90f6fa82e4226f5d32b66ef39fbb7c55765167dab60d2bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:17:12.918694Z","signature_b64":"VdQp7yLh7dKr4aYi1kRzX81k+z4AEQP0TNhdg3rQcJVxHFhswYrslrDfqkJ5hPmV+CZAD/bV8uRBpT6LSCIaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8234d9dd663ea916a90f6fa82e4226f5d32b66ef39fbb7c55765167dab60d2bc","last_reissued_at":"2026-07-05T09:17:12.918138Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:17:12.918138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.19719","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Tmqff7qaZAOmzpYS6AwpUP1w1LcqOlz+z0P22dbviiRecTAFc2alw80cUNbKTnBEZCB0/nHIeuo3fpiTbIZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:20:31.962414Z"},"content_sha256":"dd869d42ded17b07fc59512251a53c72dbff87e261dbfc0a0eba7cbcde48fb6b","schema_version":"1.0","event_id":"sha256:dd869d42ded17b07fc59512251a53c72dbff87e261dbfc0a0eba7cbcde48fb6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QI2NTXLGH2URNKIPN6UC4QRG6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The lazy (NTK) and rich ($\\mu$P) regimes: a gentle tutorial","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dhruva Karkada","submitted_at":"2024-04-30T17:11:12Z","abstract_excerpt":"A central theme of the modern machine learning paradigm is that larger neural networks achieve better performance on a variety of metrics. Theoretical analyses of these overparameterized models have recently centered around studying very wide neural networks. In this tutorial, we provide a nonrigorous but illustrative derivation of the following fact: in order to train wide networks effectively, there is only one degree of freedom in choosing hyperparameters such as the learning rate and the size of the initial weights. This degree of freedom controls the richness of training behavior: at mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19719","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.19719/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nKz39vcaIli+iZlQr1cjmY8Kfxb9fTeTWoo20NNYnPlT03mfPrZQLDDadYFTuKHJ26bDOBDvPaBZkVf7eNYGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T13:20:31.963378Z"},"content_sha256":"59d3b8fe3d174975bc778357275f72674062c7ff1815525a0cb032d3c7af934d","schema_version":"1.0","event_id":"sha256:59d3b8fe3d174975bc778357275f72674062c7ff1815525a0cb032d3c7af934d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/bundle.json","state_url":"https://pith.science/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-18T13:20:31Z","links":{"resolver":"https://pith.science/pith/QI2NTXLGH2URNKIPN6UC4QRG6X","bundle":"https://pith.science/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/bundle.json","state":"https://pith.science/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QI2NTXLGH2URNKIPN6UC4QRG6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QI2NTXLGH2URNKIPN6UC4QRG6X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ec359d4dee08c966bb9cd909e2e8bb4815354111fdc4bdd59f227de94459e4cf","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-30T17:11:12Z","title_canon_sha256":"0a518d8d410c9a4554288a814d1b2708d661caa016cb18a6485e12f4620e67f1"},"schema_version":"1.0","source":{"id":"2404.19719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19719","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19719v2","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19719","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"QI2NTXLGH2UR","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"QI2NTXLGH2URNKIP","created_at":"2026-07-05T09:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"QI2NTXLG","created_at":"2026-07-05T09:17:12Z"}],"graph_snapshots":[{"event_id":"sha256:59d3b8fe3d174975bc778357275f72674062c7ff1815525a0cb032d3c7af934d","target":"graph","created_at":"2026-07-05T09:17:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.19719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A central theme of the modern machine learning paradigm is that larger neural networks achieve better performance on a variety of metrics. Theoretical analyses of these overparameterized models have recently centered around studying very wide neural networks. In this tutorial, we provide a nonrigorous but illustrative derivation of the following fact: in order to train wide networks effectively, there is only one degree of freedom in choosing hyperparameters such as the learning rate and the size of the initial weights. This degree of freedom controls the richness of training behavior: at mini","authors_text":"Dhruva Karkada","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-30T17:11:12Z","title":"The lazy (NTK) and rich ($\\mu$P) regimes: a gentle tutorial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19719","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dd869d42ded17b07fc59512251a53c72dbff87e261dbfc0a0eba7cbcde48fb6b","target":"record","created_at":"2026-07-05T09:17:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ec359d4dee08c966bb9cd909e2e8bb4815354111fdc4bdd59f227de94459e4cf","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-30T17:11:12Z","title_canon_sha256":"0a518d8d410c9a4554288a814d1b2708d661caa016cb18a6485e12f4620e67f1"},"schema_version":"1.0","source":{"id":"2404.19719","kind":"arxiv","version":2}},"canonical_sha256":"8234d9dd663ea916a90f6fa82e4226f5d32b66ef39fbb7c55765167dab60d2bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8234d9dd663ea916a90f6fa82e4226f5d32b66ef39fbb7c55765167dab60d2bc","first_computed_at":"2026-07-05T09:17:12.918138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:17:12.918138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdQp7yLh7dKr4aYi1kRzX81k+z4AEQP0TNhdg3rQcJVxHFhswYrslrDfqkJ5hPmV+CZAD/bV8uRBpT6LSCIaAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:17:12.918694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd869d42ded17b07fc59512251a53c72dbff87e261dbfc0a0eba7cbcde48fb6b","sha256:59d3b8fe3d174975bc778357275f72674062c7ff1815525a0cb032d3c7af934d"],"state_sha256":"ff71bd8556ad3e1ce39bf75d5081c145c4acb9d18a968d500a2cb34fa2b7ab7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hHrq1tCcYyO8MFTjEZmsD5O4C4eKckmYG/YGNIozQidhoJPJknh553t8aUv6HK1dXcmySFUaZ7LOUQ/LxlsDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T13:20:31.983038Z","bundle_sha256":"e7cdf8d6e72a039b8bdebed88d13eaad8edcca87a7c232b9e982007a4bb6363e"}}